-고자

-고자 states the purpose or intention behind an action in a formal, written style, like 'in order to' or 'with the aim of'.

목적·의도Purpose, plans & wishes

Han: -고자 is formal and written; in casual speech with friends it sounds unnatural, so -(으)려고 is used.

Examples

저는 한국 문화를 더 깊이 이해하고자 한국어를 공부하기 시작했습니다.I started studying Korean in order to understand Korean culture more deeply.

이번 회의에서는 예산 문제에 대해 논의하고자 합니다.In this meeting we intend to discuss the budget issue.

정부는 청년 실업 문제를 해결하고자 다양한 정책을 추진하고 있다.The government is pursuing various policies in order to solve youth unemployment.

오늘은 새로운 제품을 소개하고자 이 자리를 마련했습니다.We have organized this event today in order to introduce our new product.

-고자vs-(으)러-(으)러 must be followed by a movement verb like 가다/오다/다니다; -고자 can be followed by any verb: 책을 사러 서점에 가요.

V+고자

V+고자 하다

알리다 → 알리고자 → 알리고자 합니다

The subject of the -고자 clause and of the main clause is usually the same person.
Attach it to a bare verb stem; do not put past -았/었- before it (✗ 말했고자). Tense is shown in the main clause.
It is formal: typical of speeches, reports, news and official writing. In casual conversation it sounds stiff, so use -(으)려고 instead.
At the end of a sentence it appears as -고자 하다 (e.g. 말씀드리고자 합니다), a polite way to announce what you intend to do.

Wrong: ~~나 주말에 친구랑 영화 보고자 해.~~

Right: 나 주말에 친구랑 영화 보려고 해.

-고자 is formal and written; in casual speech with friends it sounds unnatural, so -(으)려고 is used.

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